In this paper I analyze a contentious debate between proponents of coalescence methods
and proponents of concatenation methods for phylogenetic inference. First, I clarify
claims that phylogenetics can be reduced to genetics, and that concatenation can be
reduced to coalescence. Concatenation can be mathematically reduced to a special case
of the coalescent model by specifying parameters in the coalescent model to match
empirical assumptions made by concatenation methods. Concatenation proponents claim
that empirically realistic application of coalescent methods will amount to concatenation,
but these claims have not been adequately supported. The shape of this debate reiterates
earlier arguments that resulted in the mathematical reduction of parsimony to maximum
likelihood. Proponents of concatenation appeal to many of the same philosophical claims
that were used to justify parsimony, while coalescence models are a natural extension
of the maximum likelihood framework. In light of the historical development of methods
of phylogenetic inference, these debates can be interpreted as conflict points between
competing paradigms. The asymmetry in arguments about reduction suggests that concatenation
(an outgrowth of total evidence) is a paradigm in decline.